Note that the density \(p(\mathbf {y}|\mathbf {u})\)  still involves inverting the matrix of size \(n\times n\)  and hence is expensive to compute. Therefore, this density is approximated using the evidence lower bound (ELBO) [1]} as
\(p(\mathbf {y}|\mathbf {u}) \ge \mathbb {E}_{p(\mathbf {f}|\mathbf {u})} \left[ p(\mathbf {y}|\mathbf {f})\right].\) 
